Something that is "contagious" spreads from one person to another. The main use of the word "contagious" is to talk about diseases:
There's absolutely no reason to worry about coming in contact with a person with ALS. It's not contagious.
A "contagious" disease spreads from one person to another. We also talk about some emotions as being "contagious". One of these emotions is enthusiasm, as you can see from the example at top. Some other emotions and actions that are said to be contagious are: